Loading…

N‐dimensional wave packet transform and associated uncertainty principles in the free metaplectic transform domain

The free metaplectic transformation (FMT) is an n$$ n $$‐dimensional linear canonical transform. This transform is much useful, especially in multidimensional signal processing and applications. In this paper, our aim is to achieve an efficient time‐frequency representation of higher‐dimensional non...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-11, Vol.47 (17), p.13199-13220
Main Authors: Dar, Aamir Hamid, Bhat, Mohammad Younus
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The free metaplectic transformation (FMT) is an n$$ n $$‐dimensional linear canonical transform. This transform is much useful, especially in multidimensional signal processing and applications. In this paper, our aim is to achieve an efficient time‐frequency representation of higher‐dimensional nonstationary signals by introducing the novel free metaplectic wave packet transform (FM‐WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$, based on the elegant convolution structure associated with the free metaplectic transforms. The FM‐WPT preserves the properties of classical wave packet transform (WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$ and has better mathematical properties. Further, the validity of the proposed transform is demonstrated via a lucid example. The preliminary analysis encompasses the derivation of fundamental properties of the novel FM‐WPT, including boundedness, reconstruction formula, Moyal's formula, and the reproducing kernel. To extend the scope of the study, we formulate several uncertainty inequalities, including Lieb's inequality, Pitt's inequality, logarithmic inequality, Heisenberg's uncertainty inequality, and Nazarov's uncertainty inequality for the proposed transform.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9723